Modified fuzzy C-means and K-means clustering based spectrum sensing using cooperative spectrum for cognitive radio networks applications

Abstract

The recent decade has seen a rapid evolution of communication technologies and standards with the ultimate goal of providing global users with seamless connectivity a data access. Conventional methods of communication have been completely replaced by state-of-the-art hand-held gadgets and portable devices that enable users to communicate at high transmission rates. However, as high-end devices and gadgets become more popular and their demand for operating frequency which is essentially the Radio Frequency (RF) band in the EM (Electro Magnetic) spectrum tends to force the limits to the higher end of the RF spectrum. Due to the limitation of RF band availability, a spectrum is constructed for the requesting user for promising solution, and a difficult task. The emerging cognitive radio networks are a set of intelligent tools and scheme of identify the vacant spots in the band through effective sensing and allocating the spectrum to the requesting users. A modified cluster-based model has been proposed as part of extensive research on spectrum sensing. In the proposed work, a two-phase clustering model in the form of modified Fuzzy C-Means (FCM), and K-Means clustering is used, in which FCM is used as a training module on the channel features. K-Means is effectively used as an unsupervised classifier model. The proposed classification model was tested in a densely populated cognitive radio network compared to standard methods such as SVM (Support Vector Machine), FCM, and K-Means. Superior performance in terms of quality metrics like 90% classification accuracy, 91% spectral utility 90% are notable findings of this research work.

Keywords

Cognitive radio network clustering spectrum utilization support vector machine fuzzy C-means K-means

1 Introduction

Recently, the demand in accessing the internet-based applications by various sectors has been increased exponentially thereby the growth in network traffic has initiated development in the next generation of wireless communication networks. The growing number of users, devices, and systems for accessing data-intensive applications necessitates the introduction of 5G-based communication networks, which overcome the difficulties encountered by the existing 3 G and 4 G technologies. In today’s business world, the use of wireless devices increases tremendously in various sectors. The existing technologies 3 G,4 G, and other wireless systems satisfy the necessities of high coverage and availability of the wireless networks by introducing more intense networks. In recent years the requirement of accessing Internet of Things (IoT) services related with the machine to machine communication increased in multifarious times. The next-generation wireless technology is driven by technology and requires low power, low throughput devices with a long battery lifetime, as well as a new radio technology specification for data rates, latency, and other key parameters. This leads to the way for introducing 5 G wireless technology in communication systems.

A new broadband cellular communication standard for a mobile device that has a great impact on the wireless network termed as 5 G [1] is introduced. The speed and the bandwidth of 5 G enhance the frequency of the Ultra Wide-band up to 300 GHz to carry out and deliver the message that provides better performance in throughput than the 4 G LTE (Long-Term-Evolution). The higher frequency is required, while the number of users and data to be accessed through 5 G increased. Beam forming technology is enabled by the requirement of having more small-sized antennas on both the transmitter and receiver sides. At the same time, the beam out over a short distance causes a denser network in cities.

IoT of 5 G encompasses the features of devices and services as a single element that benefits the user to introduce 5 G to the home and business through the wired connection as used in today’s environment. A huge amount of spectrum is necessitated to handle this increasing number of wireless devices. The availability of the spectrum is a limited resource. Nowadays, it is very difficult to find the free spectrum that meet the future needs of handling a huge volume of wireless devices and data traffic. Wireless carriers need higher spectrum bands in order to build the 5 G networks and radio technology that effectively uses the spectrum band. Cognitive radio technology is introduced in 5 G standards to facilitate the dynamic spectrum allocation between the entities of the networks. The cognitive technology can meet the main requirements of 5 G standards such as higher throughput, higher availability and coverage, handling a large number of users, and higher spectral efficiency.

Cognitive radio [2] is an innovative technology that detects whether the communication channels are in use or not, allowing users to shift to less-used channels as other channels become overcrowded. The objective of this technology is to minimize the interference among the users of the channel and enable the unlicensed users to access the spectrum. Usually, the users of the channel can be classified into primary and secondary users. The primary user is the user who has the legacy right to access the specific part of the spectrum, or simply the licensed user of the spectrum part. The secondary user is an unlicensed user or a user who does not have the legacy right. The main objective of cognitive radio technology is to find the unused spectrum and allocate it to the unlicensed user. Spectrum sensing is one of the techniques that perform the dynamic allocation of the channel in an effective manner when compared to other techniques such as spectrum database and pilot channel.

The fundamental process of spectrum allocation is accomplished through the licensing process. But the spectrum inefficiency is occurred due to some licensed frequency bands being underutilized while others are over-utilized as shown in Fig. 1. For example, GSM cellular users who do not have access to spectrum can obtain permission to use TV spectrum frequency bands. Recently, various spectrum sensing techniques have evolved for cognitive radio networks to improve spectrum utilization. Scheduling of compressed sensing provides the advantages of spectrum sensing and periodic detection, which reduces the sensing overhead in cognitive radio networks [3]. Eigen value-based mean to square model examines the smallest and largest eigenvalues of the covariance matrix to figure out the spectrum status [4]. The maximum and minimum Eigenvalue-based sensing procedure includes an iterative power method to minimize the computation issues in spectrum sensing [5]. Machine learning-based cooperative spectrum sensing procedures identify the optimal position for sensing node placement to enhance the spectrum sensing ability [6]. Bidirectional decision-based wideband spectrum sensing procedure considers the normalized power spectrum and identifies the occupied bands through a search process. The sequence-based search is performed forwardly and backwardly to obtain the final decision based on the Neyman Pearson criterion [7].

Fig. 1

Spectrum Inefficiency usage among Licensed Users [Source:https://www.wipro.com/engineeringNXT/cognitive-radio/]).

Energy detection-based spectrum sensing detects the spectrum status in the presence of Rician statistical nature to obtain better performance through self-interference cancellation [8]. The issues in multi-antenna cognitive radio networks are addressed in [9], and present an SVM-based signal classification model. The user conditions are classified and multiple alternative solutions are provided using an error-correcting output code-based SVM model. SVM exhibits better performance in spectrum whole detection. Prediction and sensing-based spectrum management models investigate the base station beam forming and sensing time to maximize the sum rate of secondary users [10]. In this paper, a novel Fuzzy CK-means clustering-based dynamic spectrum sensing algorithm for radio spectrum sensing is elaborated and the results are analyzed with the existing cluster-based algorithm. The major objective of this research work is to enhance spectrum utilization by reducing the sensing time and increasing sensing accuracy to the Secondary users. Efficient spectrum sensing improves the spectrum utilization and overall performance of the cognitive radio network. The summarized contributions of this research work are presented as follows.

Presented an efficient mechanisms scheme for CSS sensing best quality data based on cluster and parallel reporting mechanisms to enhance the data reporting.

To improve the spectrum sensing, a modified fuzzy CK-means algorithm has been presented.

Experimental analysis of the proposed modified fuzzy CK-means algorithm is presented to validate the performances through various network parameters like spectrum utilization, throughput, false alarm rate, classification accuracy.

Comparative analysis of the proposed model with benchmark techniques like SVM, FCM, and k-means algorithm is presented for better validation.

The remaining part of the research work is arranged in the following manner. Section II provides a review of existing methodologies. Section III illustrates the implementation of the Fuzzy C-means algorithm for allocation of spectrum dynamically. Section IV analyses the experimental outcomes and findings on the experimentation carried out in the work. Finally, Section V concludes the research work.

2 Related work

Spectrum sensing techniques for channel allocation can be classified into two categories, named Non-cooperative and Cooperative as shown in Fig. 2. Non-cooperative sensing techniques process on their own. The sensing technique is executed based on signal detection and preloaded information. Cooperative sensing techniques are implemented on the basis of the concept of sharing sensing information among users, and allocation decisions are made based on the control unit and the mesh type of network.

Fig. 2

Classification of spectrum sensing technique [11].

A cooperative spectrum sensing is an effective scheme proposed to enhance spectrum utilization. The Cooperative Spectrum Sensing (CSS) techniques comprise of three main phases such as local sensing, reporting and fusion center. The overall performance of the CSS technique depends on the accuracy of local sensing, reliability of the reporting channel, the data fusion techniques and the network overhead. The sensing performance can be increased by allowing only a certain number of cognitive users to sense the channel with the highest Signal to Noise Ratio [12]. Clustering techniques have been adopted for improving the performance of sensing of CSS for cognitive radio networks. The Cognitive users are grouped into clusters and the user with the highest SNR value is chosen [7] as the cluster head which in turn sends the cluster decision to FC [13] as shown in Fig. 3. The cluster-based cooperative spectrum sensing (CSS) scheme produces high accuracy in spectrum detection [14-15]. The conventional clustering mechanism is time-consuming and inefficient because a secondary user [16] is chosen as a cluster head and must deal with a large amount of data [17]. To overcome these issues, a sensing time-saving cluster-based (STSC) [18] CSS is proposed to decrease the burden of the secondary user in the data processing. The sequential tests can be applied over the cluster head or fusion center. The sensing time can be drastically reduced by determining the credential capability of each secondary user and deciding whether or not the cluster head can be added with the secondary user. The proposed scheme reduces the sensing time at most 88.5% by reducing the sample size.

Fig. 3

Cluster based cooperative sensing model [21].

A selective method-based cluster approach is proposed [19] to reduce the reporting time and bandwidth while the sensing level is maintained within a certain limit. The clusters are systematized by sensing the best signal-to-noise (SNR) ratio value in the primary signal and the frequency division-based parallel reporting mechanisms are proposed to reduce the reporting time. The cluster head is selected dynamically based on the sensing qualities of the cognitive radio users. The optimal Chair-Vashney rule is applied in each fusion center to obtain a highly sensing node based on the SNR value. Another issue with the cluster-based CSS is that a cluster located further away from the FC has the characteristics of reliability in local sensing decisions but a low SNR reporting channel. Due to this reason, the performance of the CSS of cooperative radio networks is reduced further. A novel technique called multi-hop [20] cluster-based CSS is introduced to avoid error reporting and reduce energy consumption. In this technique, apply the concept of dividing the clusters into multilevel based on the distance of cluster heads and fusion center, so that it attains the benefits of more energy consumption. The impact of transmission power on the energy efficiency and probability of false alarm has been reduced by introducing a framework that optimizes the design parameters.

An iterative algorithm [22] is proposed to determine the optimal design parameters for the CSS system. The optimal problem that reduces the energy efficiency is devised as a function of two parameters in which the first parameter denotes the combination of sensing time and transmission time while the second parameter represents the number of Cognitive radio users. A novel mechanism for grouping nodes based on the SNR value between nodes or between the primary user and the node, as well as the correlation between nodes that are in the same area and experienced similar conditions, allowing them to be correlated. A merged clustering measure is presented, and a correlation-based clustering procedure [23] is implemented and evaluated. An Intelligent CSS [24] scheme based on Bayesian Learning is proposed to improve the sensing performance both in inter-cluster CSS and Intra-cluster CSS. The cluster decision of each node is collected by the cluster heads and transmitted to the fusion center in the allocated sub-slot. The fusion center makes the final decision based on the information collected from all the cluster heads. An optimal sensing value of intra-cluster CSS are obtained by minimizing the total Bayesian learning cost defined by the rate loss. The total false alarm probability and detection probability of inter-cluster CSS are obtained by means of Bayesian fusion. K-means clustering algorithm is proposed to cluster the nodes and the cluster head is selected for each cluster.

The major issue in the CSS scheme mainly lies in the clustering of nodes by measuring the similarity of the nodes and selecting the cluster head for each node which improve the performance of sensing by producing accurate reports about the sensing information and decision. The quality of the cluster analysis [25] depends on two factors like type of clustering techniques and implementation. K-means is a clustering algorithm [26] that decides that partitions a given dataset into K-clusters [27, 28]. The k value must be known prior to the cluster construction [29]. It has the advantages of being fast, robust, and simple to implement. But it has the disadvantages of not being invariant to linear data transformation [31] and also not being successful in finding overlapping clusters [32]. Due to this, the representation of a specific dataset with polar coordinates and Cartesian coordinates [30] can produce different results. K-means is not suitable for noisy and nonlinear data. The fuzzy clustering [33 –45] can be improved based on reducing the number of distance computations by checking the value of the membership for each point. If the value of the membership is less than the threshold value, then the point will be eliminated from the clustering.

3 Proposed work

Cognitive radio networks formulate the given scenario into two major components namely the primary users (PU) and secondary users (SU). While the former reflects the licensed band of users whereas the latter reflects the unlicensed band of users. PUs has unconditional access to the RF band while SUs must seek out the opportunity for vacant spaces in the spectrum as and when a PU switches over to the IDLE channel (or) OFF state. In general, PUs in the IDLE state may return to the ACTIVE state at will whenever required and in such cases, the existing SUs utilizing their band should be relocated to another vacant space. All these functions are effectively handled by means of the cognitive cycle comprising of sensing, aggregations of sensed information and the decision taken related to the presence/absence of PU in the sensed channel based on the information aggregated by the sensing nodes. The spectrum must be allocated in such a way that there are no interference effects between PUs and SUs, which could result in signal degradation, defeating the entire purpose of quality communication. The cognitive cycle [19] is depicted in Fig. 4 below as a continuous process.

Fig. 4

Illustration of cognitive cycle [34].

An observed Fig. 4, the process of cognitive-based spectrum allocation has to be continuous and depends on the sensing efficiency and the nature of decision-making performed in the decision fusion center. Considering a signal being transmitted from the base station (BS) to be as m (t) with channel noise σ with zero mean and variance, the received signal could be expressed as

$r (t) = m (t) + σ$ (1)

The cognitive cycle is all about continuous sensing of the input signal received to define the presence or absence of the primary user activity in the sensed signal r (t). This causes the problem formulation in the proposed case to converge onto a binary hypothesis problem formulated as $H (t) = 1; ifr (t) = m (t) + σ$ (2)

And $H (t) = 0; ifr (t) = σ$ (3)

Equations (2) and (3) could also be alternately formulated as the probability formulation as P (H₀) = ∅ ₀ = 0 and P (H₀) = ∅ ₀ = 1 which defines the occurrence of that particular event. In the proposed work, the objective of determination of primary user activity as per (1) and (2) is approached through an indirect machine learning approach using a hybrid joint framework of two powerful and efficient cluster-based mechanisms, namely, the Fuzzy C-Means and K-Means, which in the proposed work is termed as the FCK-Means. The motivation lies in reducing the computation complexity of direct machine learning methods like neural network-based models and alternately utilizing the complexity reduction-oriented clustering models. The first phase of the work is based on FCM for partitions of class labels based on analysis of the received signal strength and utilizing this data for training the model. These partitions are fed into the second stage of clustering through K-Means which is used as a classifier model with two objective output classes corresponding to H₀ & H₁.

The flow process of the proposed FCK-Means spectrum sensing methodology is projected in Fig. 5 shown. As mentioned in previous sections, FCM is used for the training process where data related to channel characteristics are taken from a known environment to generate the test data. After preprocessing and feature extraction, the samples are given to the Fuzzy C- Means module. FCM operates on the test data to generate output classes specified according to the number of objects or target objects defined. In the proposed case in Fig. 5, the general terminology of P clusters is utilized. The output objects are given as train data to the K-Means module which forms the second phase of the proposed work. In K-Means the data from the unknown environment or the real-time sensing of information related to channel state is given as another input. These data points are clustered into two object classes namely, presence of PU and absence of PU.

Fig. 5

Flow diagram of the proposed FCK-Means of spectrum sensing.

The motivation behind using the double stage of clustering is observed from literature studies that FCM performs hard thresholding in standalone configuration and is not suitable for large data sets. In the second phase of the proposed model, the train data generated from FCM is used to train the K-means classifier which operates on the data from the unknown environment and process them or clusters them based on the knowledge imparted to it. This is processed by the FCM training data and classifies the given data points into one of the two output classes.

The double stage of clustering helps to improve the accuracy of classification or in other words, reduces the probability of false alarm detection to a great extent. Due to the training imparted to the K-means, it can also study the incoming stream of sensed information to detect any PU mitigation attacks which is an added feature.

Considering an input stream of received signal strength data from the known environment or the unknown data, the data points could be modeled as $r (t) = r_{1}, r_{2}, r_{3}, \dots \dots \dots \dots . r_{N}$ (4)

In terms of the feature vector, (3) could be modeled as $\vec{R} = {r_{1}, r_{2}, r_{3}, \dots \dots \dots \dots . r_{N}}$ (5)

Where N denotes the length or the number of features. This feature vector $\vec{R}$ is applied to the Fuzzy C- Means algorithm to provide F non-overlapping clusters or subsets or classes denoted as F_c, where c denotes the class number. The pseudo-code of the Fuzzy C –means could be summarized as,

Table 2

Input : \vec{R} = {r_{1}, r_{2}, r_{3}, \dots \dots \dots \dots . r_{N}}

Output : F_C, c = 1, 2, 3 … . . ¥ N

initialize rand (cluster (c)) , Iteration_max, CentroidsØ = rand ;

compute norm _metric = ED (r_i -Ø _j) ;

compute membership matrix {(M_{m} = \frac{1}{\sum \frac{r_{i} - Ø_{j}}{r_{i} - Ø_{k}}})}^{\frac{2}{w - 1}}

for p = 1 : iteration_max.

compute (c_new) ; min(M_m)

if abs| (min(M_m) ^p - min(M_m) ^p-1) |< ∈

then break ;

else min(M_m) ^p-1 = min(M_m) ^p

end if

end for

end

The proposed FCM is an iterative process and continues until there is no change in the cluster centers. The basic metric used for similarity measurement is the Euclidean distance (ED). As per the above-mentioned pseudo-code, random cluster numbers are selected and the cluster centroids are randomly initialized.

The normal clustering process of FCM based on the similarity of every data point to the selected cluster center or centroid is computed as the ED. Minimization of the ED metric is taken as the objective function and the cluster centers are updated at every iteration until no more change in the cluster centroid is observed. These data points under different class are formulated as training data and fed into the K-Means module whose pseudo-code is summarized below.

Table 3

Input : F_C -- object instances where c = 1, 2, 3 . . ¥ N

Output : H₀ ; H₁

begin

call KMeans (train data (F_{C}), test data (\vec{T_{k}})

end

main (KMeans)

{

initialize target classes H₀& H₁ ; K_c = cluster center ;

μ = mean ;

select K_C = rand (F_C) ;

for all k \in \vec{T_{k}}

assign K_{C} \leftarrow k; for μ (k \in \vec{T_{k}}) \approx K_{C};

compute μ_jfor all jɛK_C

repeat and update μ_j

} while k ≠ 0 ;

In the second phase of the proposed FCK-Means algorithm, the clustering methodology of K-Means is used effectively as a classifier based on its unsupervised learning features. The data generated from the FCM is used to train the K-Means process based on its which it clusters the input test data points into one of the two object classes namely H₀ & H₁. The functionalities of both FCM and K-Means are nearly similar in their approach of selection of random cluster points, centers, and computation of distance metrics. Based on the closeness and mean of each data point with its own cluster centroid, the output classes are populated with data points. The double stage clustering improves the clustering process. In K- Means, the output class, or the K- index measure is fixed as two as only two target output classes are required. In a general case, the K value depends on the number of output classes required.

An exhaustive experimentation has been done in the proposed work to justify the superiority of the proposed clustering methodology where information from all nodes or cognitive users are taken into consideration as depicted in the process flow shown in Fig. 5 to reach a decision related to the presence/absence of PU.

4 Results and discussion

A hybrid joint scheme utilizing the clustering concepts of Fuzzy C- Means and K-Means methodology has been proposed and implemented in this paper. As mentioned in previous sections, the problem formulation narrows down to a binary hypothesis problem where the objective lies in the detection of the presence or absence of primary user activity in the sensed channel. The simulations have been done exhaustively on a MATLAB environment running on an I5 2.86 GHz processor configuration with 8GB RAM capacity. The simulation settings taken for the experimentation are listed below in Table 1.

Table 1
Simulation Settings –Joint Clustering Model for CSS

Parameters Values

No of PU’s 3

No of SU’s 1000

PU transmission probability 0.5

PU distance 1000m

Bandwidth in (MHz) 5

Transmission power(W) 0.1

Noise PSD in (dBm) -153

Noise Power (W) 2.5059e-12

Type of Channel Rayleigh fading

Sensing time(ms) 500ms

Path-loss exponent 4

M X N 3x3

Structure Cooperative

Fussion Scheme Soft

Parameters	Values
No of PU’s	3
No of SU’s	1000
PU transmission probability	0.5
PU distance	1000m
Bandwidth in (MHz)	5
Transmission power(W)	0.1
Noise PSD in (dBm)	-153
Noise Power (W)	2.5059e-12
Type of Channel	Rayleigh fading
Sensing time(ms)	500ms
Path-loss exponent	4
M X N	3x3
Structure	Cooperative
Fussion Scheme	Soft

With the experimental settings mentioned in Table 1, the detection probability and false alarm probability have been taken as the primary performance evaluation metrics in the proposed work. As described in previous sections, the probability of presence/absence of PU is denoted as P (H₀) = ∅ ₀ = 0 and P (H₀) = ∅ ₀ = 1 for the absence and presence of PU activity, respectively. The outcome in the proposed work has been compared with benchmark methods involving the well–known support vector machines (SVM), Fuzzy C- Means (FCM), K- Mean’s techniques of cognitive spectrum sensing. An extensive analysis of each metric has been dealt with in this section, in detail.

Figure 6 depicts the plot of detection probability P_d against varying number of cooperative secondary users which are at a maximum of 1000 in this research work. As shown, the probability of PU detection increases with the number of SUs, which is entirely due to the double clustering process proposed in this work. The first stage output from FCM is fed as input to the unsupervised classifier namely, the K-Means, which effectively acts on the clustered partitions and groups them into any of the specified two classes. It could be observed from Fig. 6 that optimality in probability detection is achieved at around 500 users of SUs for the proposed modified FCK- Mean as against K- Means which records a P_d = 1 at 780 users, followed by FCM which records a P_d = 1 at 900 SUs and SVM with P_d = 1 at 940 users. Another interesting observation from Fig. 5 is that SVM provides a significant classification accuracy or detection probability of 0.7 for a minimum of 100 users as against the proposed FCK-Means which is records a P_d = 0.35 for 100 users. This reflects the fact that the high detection probability projected by SVM involves false alarm probabilities which are exactly reflected in the plot of the probability of false alarm against the number of secondary users count as depicted in Fig. 7.

Fig. 6

Performance of detection probability.

Fig. 7

Performance of false alarm probability detection.

Probability of False Alarm (P_FA) is an important metric that defines the number of false alarms generated during the detection of presence/absence of PU activity in the sensed channel characteristics. The inverse of the P_d plot depicted in Fig. 6. It could be observed that SVM which has projected a P_d = 0.7 at a SU count of 100 users now projects a P_FA = 1 or 100 users which are extremely high as against a P_FA = 0.98. However, initially, not much of a difference is observed. But, as the number of SU users increases, a wide deviation from the characteristics of the SVM classifier with proposed FCK-Means is observed which best defines the efficiency of correct detections in the proposed method. It could be observed that, in the proposed FCK- Means P_FA tends to decrease very steeply down to P_FA = 0.1 starting from 900 –1000 secondary users which represents a significantly dense network. However, in the same case scenario, P_FA is observed to be extremely high of nearly 1 for up to 550 users which justifies the fact that SVM alone is not able to provide the correct detection. This may result in erroneous detection which may result in increased interference of SUs and PUs subsequently leading to signal degradation. Conversely, K-Means records a P_FA = 0.55 on an average scale of increasing the number of SUs in FCM with a marginal average ofP_FA = 0.8. These are significantly high values indicating that several false detections are possible in the existing methods taken and cannot be taken to be very reliable. Figure 8 depicts that classification accuracy of the K-means classifier based on the inputs from FCM clustering of phase-I.

Fig. 8

Performance of classification accuracy.

The superior performance of 0.6 or 60% accuracy of classification is observed in the case of a small set of secondary users amounting to 100 as compared to 0.54 for SVM, 0.53 for FCM and 0.5 for K-means. An 11% improvement in classification accuracy is reported for FCK-Means when compared with SVM.A 13.2% improvement for proposed FCK- Means is observed when compared with FCM. In the proposed FCK-Means20% improvement is observed when compared with the K- Means clustering algorithm. The superior performance of 20% over conventional standalone K-Means observed in the proposed work is attributed to the fact of double classification done in proposed FCK- Means. The K-Means classifier used in the proposed work operates on the already partitioned classes of data thereby accounting for the significant improvement in classification accuracy. At high SUs, a significant improvement could be observed. For a SU count of 500 users, the classification accuracy related to the binary hypothesis is about 7.14% improvement over SVM.A 13.36% improvement is observed for proposed FCK- Means when compared with FCM and a 15.38% performance improvement is reported for proposed FCK- Means when compared with K- Means clustering algorithm. The findings in Fig. 8 are once again validated by the misclassification accuracy projected in Fig. 9 below.

Fig. 9

Performance of misclassification accuracy.

Figure 9 presents the misclassification accuracy plot for an increasing number of SU users. For a 500 SU user scenario, the misclassification accuracy of the proposed FCK-Means is reduced by over 64% when compared with the conventional K-Means. The misclassification accuracy of the proposed FCK-Means is reduced by 63% when compared with an SVM classifier model. A drastic 70% reduction is reported for FCK-Means, when compared to the FCM algorithm such as high degree of variations in the misclassification accuracy of benchmark comparison techniques observed in the proposed work. It is due to the high ratio of class label imbalances which is corrected and rectified by the double stage clustering used in the proposed work. This class imbalance occurs due to the close resemblance of the mean values to the centroids of each cluster as the features of this PUs are closely correlated with each other. For a 400 SU scenario, misclassification accuracy is reduced to 1%, with a peak misclassification rate of 24.8 % for a 100 SU user scenario. This analysis is once again reflected as the error convergence analysis which is projected in Fig. 10 shown below. The error rate is merely a parameter reflecting the overall performance of the detection and classification mechanism comprising the performances of P_d and P_FA. Performance of error rate could be observed from Fig. 10 that minimized convergence is achieved in the proposed FCK- Means which is more stable like the SVM.

Fig. 10

Performance of error rate.

Throughout the analysis, it was discovered that FCK- Means and SVM have similar operating characteristics, with marginal improvements of proposed FCK- Means over SVM, proving the effective nature of SVM. However, the well-known fact that SVMs are not quite optimal for large data sets becomes a limiting factor in their performance in the proposed work. This hypothesis could be well-validated by observing the performances of SVM which exhibit a classification accuracy of 53% for a 100-user scenario against an84% classification accuracy observed for a 1000 user scenario. This is significantly lower than the proposed FCK-Means model, which projects a 64% accuracy for a 100-user scenario and a 90% classification accuracy for a 1000-user scenario. Hence, the proposed FCK-Means proves itself to be an ideal detector for large and dense networks characterized by large data sets in terms of their channel characteristics. The throughput analysis is another important performance metric computed and projected in Fig. 11. This is usually expressed in bps/Hz. The average throughput is analyzed against increased number of SUs or cooperative/cognitive users taking part in the communication process. Throughput and P_d (Probability of detection) are inversely related as increased P_d typically in the ideal case of P_d = 1 indicates the presence of PU in the communication and the lack of available spectrum holes for the SUs to communicate.

Fig. 11

Performance of throughput analysis.

This protects the PUs from the interference effects of the SUs. However, in the analysis projected in Fig. 11, it can also be interpreted that, increasing accuracy of detection or classification accuracy reflects in the throughput improved as a greater number of SUs users are able to take part in the communication process thus causing more transmission of the information packets. Near-optimal performance is observed in both FCK- Means and SVM. The difference in classification accuracy between proposed FCK- Means and other methods records for the slight and marginal variation over other methods. Sensing time analysis is a measure of the time taken by the cognitive users to sense the presence/absence of PU activity in the channel. The analysis projected in Fig. 12 is closely correlated with P_d (Detection probabilities) and P_FA (Probability of False Alarm).

Fig. 12

Sensing time analysis.

As compared to Figs. 12, the peak occurs when the number of cognitive users is 500 at which the detection probability P_d nearly equals 1. On the contrary, the increased sensing time at 500 users also exhibits a reduced P_FA = 0.2 as observed in Fig. 7. In general, it could be inferred from the analysis that increased sensing time by the CRs helps in better detection of presence of PUs in the channel. Sensing time is essentially an important metric as it plays a key role in the reduction of P_FA. This is significant especially in learning-based models, as learning about the presence/absence of PU in the channel in the sensing period/time is fed back to the training in order to reduce the error probability or probability of false detection. As with other methods, FCM and K-means exhibit high sensing times which reflect the increased waiting time to detect PU activity in the channel and the inefficiency of the sensing process. This may result in increased false alarm probability with reduced classification accuracy as justified in previous plots. A final analysis is done based on the spectral utilization in proposed modified FCK- Means compared against benchmark methods.

This is an overall estimate or validation metric that effectively determines the efficiency of the spectrum sensing model because the goal is to maximize spectrum utility at the beginning of scarcity. This is highly dependent on high detection probability rates and reduced false alarm probabilities. It could be clearly observed from Fig. 13 shows that, spectrum utilization improved with increasing SUs. Initially, the FCK- Means record slow spectral utility due to low values of detection probability and a significantly high value of false alarm probability. However, at users exceeding 500 CRs, the efficiency of spectral utility reaches 90% for FCK- Means, an 88% spectral utility for SVM-based classifier and a reduced 85.1% for FCM method. K-Means has an 83 % spectral utility, indicating that the proposed work is superior. In other words, a better detection probability ensures that increased number of SUs can transmit and communicate during the OFF states of PUs. The reallocation of licensed band to PUs on their return to ACTIVE state thus accounting for the superior performance recorded in Fig. 13. The entire analysis has been done with respect to the impact of a varying number of cognitive users on the given model scenario.

Fig. 13

Performance analysis of spectrum utilization.

5 Conclusion

Cognitive radio networks are an emerging class of intelligent methods that are capable of intelligent and optimal allocation of the scarcely available radio frequency spectrum to the licensed and unlicensed band of users. With the increasing demand for the utility of high-end devices requiring the upper band of RF, CRs provide a promising solution for optimal spectral allocation. A joint framework model comprising of Fuzzy C-Means and the K-Means is used in the proposed work. The proposed work determines the exploitation of the powerful features of clustering methodologies for either clustering or grouping and classification. In the proposed work, two-phase clustering is done. The input channel features are used as training data on the Fuzzy C- Means to group them into their class labels which are acted on by the K-Means given a two-class objective to group them into classes labels of either P (H₀) = ∅ ₀ = 0 or P (H₀) = ∅ ₀ = 1. The experimentation results have been accomplished on large data sets and compared with well-known and efficient benchmark methods like SVM, FCM and K-means in a stand-alone mode of operation.

The valuation has been conducted over critical performance metrics like Detection Probability, False alarm detection, classification accuracy, error convergence and spectrum utilization. It could be observed that FCK- Means outperforms the other methods by a satisfactory margin. SVM closely competes with the proposed FCK- Means but is found to exhibit poor performance when the number of SUs increases or the classes become large. A 91% spectral efficiency is reported for the proposed FCK- Means method which offers to be a promising solution for future research. In this research work, the signal-to-noise channel characteristics are accepted to be improved in the presence of AWGN with zero mean and variance. In future work, it could be investigated in improving the cluster-based model with hybrid combinations of optimization methods to fine-tune the accuracy of the proposed work. Reduced classification accuracy and detection probability for a small number of SUs are observed to be limitations in the proposed work, which could be addressed in future work.

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